Question

Q7:

There is a large supply of light bulbs with the average life of 1000 hours and the standard deviation of 50 hours.

1. A light bulb is drawn at random. Find the probability that it will last more than 1020 hours.
2. A random sample of 25 light bulbs is drawn. Find the probability that the sample average life is more than 1020 hours.

Answer 1

Part a

X =1020

P( X > 1020)

Z score

P( X > 1020) = P( Z > 0.4) = 1-P( X<0.4)

Using Z table or excel commnd =NORMSDIST( 0.4)

P( Z< 0.4) = 0.6554

P( X > 1020) = P( Z > 0.4) = 1-P( X<0.4) =1- 0.6554 = 0.3446

Answer :

the probability that randomly selected bulb will last more than 1020 hours is 0.3446

Part b

X =1020

n = 25

Z score

= P( Z > 2) = 1-P( X< 2)

Using Z table or excel commnd =NORMSDIST( 2)

P( Z< 2) = 0.9772

= P( Z > 2) = 1-P( X<2) =1- 0.9772 = 0.0228

Answer :

the probability that randomly selected 25 bulbs will last more than 1020 hours is 0.0228